What should be added` x + 2 y + z,` so that the sum be z

Options

A. `x + 2y`
B. `- (x + 2y)`
C. `x -2 y`
D. `- x + 2y`

Answer

To solve the problem, we need to determine what should be added to the expression \( x + 2y + z \) so that the result equals \( z \).

### Step-by-Step Solution:

1. **Set Up the Equation**:
We need to find a value \( a \) such that:
\[ (x + 2y + z) + a = z \]

2. **Isolate \( a \)**:
To find \( a \), we can rearrange the equation:
\[ a = z - (x + 2y + z) \]

3. **Simplify the Right Side**:
Now, simplify the right side of the equation:
\[ a = z - x - 2y - z \]
Here, the \( z \) terms cancel out:
\[ a = -x - 2y \]

4. **Final Result**:
Therefore, the value that should be added to \( x + 2y + z \) to make the sum equal to \( z \) is:
\[ a = -x - 2y \]

### Conclusion:
The answer is \( -x - 2y \).

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